Increasing function, partial derivatives

I must say the veracity of the following statement : If $\displaystyle f:\mathbb{R}^2 \to \mathbb{R}$ differentiable such that $\displaystyle f_x(x,y)>0$ and $\displaystyle f_y(x,y)>0 \forall (x,y) \in \mathbb{R}^2$, then $\displaystyle g(t)=f(t,t^3)$ is an increasing function.
My attempt : I don't know how to start. By intuition it's false, so that the exercise show me a difference between one variable functions and several variables functions. I've not found any counter example yet. So it might be true, but I don't know how to prove it.
Any tip will be appreciated. (Not a full answer please)

I must say the veracity of the following statement : If $\displaystyle f:\mathbb{R}^2 \to \mathbb{R}$ differentiable such that $\displaystyle f_x(x,y)>0$ and $\displaystyle f_y(x,y)>0 \forall (x,y) \in \mathbb{R}^2$, then $\displaystyle g(t)=f(t,t^3)$ is an increasing function.
My attempt : I don't know how to start. By intuition it's false, so that the exercise show me a difference between one variable functions and several variables functions. I've not found any counter example yet. So it might be true, but I don't know how to prove it.
Any tip will be appreciated. (Not a full answer please)